Early prime movers or power sources such as the mill stream water wheel; and, later the steam engine, created a need for transferring power from one place to another through torque transfer. An early example of torque transfer was the belt and pulley assembly, frequently utilized in machine shops to drive various machines.
The early prime movers generated low revolutions per minute (rpm) and mechanically simple torque transfer mechanisms were capable of creating very little power. In portable machines, chains and sprockets are often used to transfer power. The most common example of this form of torque transfer is the ordinary bicycle. The bicycle sprocket and chain are a roller cam assembly; and the relative motion between the roller in the chain and the sprocket is that of an involute. It is the shape of the sprocket that enables the power to be transferred smoothly.
With the need to transfer torque between adjacent parallel and perpendicular shafts, something else had to be devised. In fact, the old water wheels that were used to grind grain employed wooden pegs as gear teeth to transfer torque; but, as rpm and torque increased, it was observed that a fluctuation in speeds occurred, creating destructive forces. This fluctuation resulted from the variations during rotation of the effective radii between the meshing of the pegged wheels.
The variation of the effective radii was a result of the shape of the pegs. The first solution was to develop a double cycloid tooth with a convex shape above the pitch circle and a concave shape below the pitch circle. These gears looked something like a plurality of rollers evenly spaced with their axes parallel to the input shaft and attached to the surface of a wheel. If two concave arcs were placed near the point of attachment and the surface of the wheel, it would create a tooth that resembled the teeth used in these gears. This design solved the velocity fluctuations. However, the gears were difficult to manufacture and their shape made them highly susceptible to failure.
In the latter part of the nineteenth century, the involute gear was developed. It was both much stronger and cheaper to make. In calculations of gear strength, the teeth were treated as a series of cantilevered beams, and an engineer named Lewis devised a table of values called the Lewis Form Factor that simplified calculations of torque capacity of spur gears. This table is used in calculations today.